G_2型量子群表示的Grbner-Shirshov基  

Grbner-Shirshov Basis Represented by G_2-Type Quantum Group

作　　者：艾尼.吾司塔 阿布都卡的.吾甫 

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046

出　　处：《重庆工商大学学报（自然科学版）》2013年第11期1-5,共5页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：国家自然科学基金(11061033)

摘　　要：用单李代数的泛包络代数表示的Grbner-Shirshov基方法,也就是Grbner-Shirshov对(pair)方法,来构造G2型量子群表示的Grbner-Shirshov基是非常苦难的。而用双自由模方法来构造G2型量子群的有限维不可约表示的Grbner-Shirshov基是非常方便的;以已知的G2型量子群的Grbner-Shirshov基为基础,用双自由模方法构造G2型量子群的不可约表示的Grbner-Shirshov基。The construction of Grobner-Shirshov Basis represented by G2-type quantum group by Grobner- Shirshov Basis method represented by universal enveloping algebras of simple Lie algebras, i.e. Grobner-Shirshov pair method, is very difficult, however, the construction of Grobner-Shirshov Basis represented by finite dimensional irreducible of G2-type quantum group by double free modules is convenient. By taking Grobner- Shirshov Basis of G2-type quantum group as the basis, this paper uses double free modules method to construct Grobner-Shirshov Basis of irreducible representation of G2-type quantum group.

关 键 词：量子群 Grsbner—Shirshov基 合成 双自由模 最高权模 

分 类 号：O151[理学—数学]